4.26 A bookseller receives 4 copies of a magazine every week. On average. 3 customers show up per week looking for a copy of the magazine, according to a Poisson process. It is assumed that copies not sold in one week cannot be sold the following week.
a) What is the probability that the bookseller will sell all received copies of the magazine in a given week?
b) What is the probability that in a month (4 weeks), there is at least one week during which the bookseller does not sell all the copies of the magazine?
c) Determine the mean and variance of the number of copies of the magazine sold in a week.
d) Determine the average number of customers who do not get a copy of the magazine in a week.